How Many Possible Real Games?

Theoretically, the number of possible games is huge according to Shannon and even bigger according to Hardy. Something like 10^120 and 10^10^50.

https://herculeschess.com/how-many-chess-games-are-possible/

But they only estimate assuming raw equivalence for every piece.

Realistically, there are way fewer possible games if played intentionally. There are only a handful of non-foolish opening moves, second moves, etc. Several opening styles are favorites such that everything else would lead to weak positions and nobody really plays them. Let's not count the random meaningless games where neither side has intention to win.

Wouldn't the actual number of possible (or probable) games be manageable enough for a modern computer to categorize and identify instantly? And so all current and future real games are mere repeats of games played already at some point by somebody in the past. We're only repeating history, not playing new games!

Some beginners could be sitting down and unwittingly, inadvertently, randomly, repeating one of the great championship matches of Fisher-Spassky, Kasparov-Karpov, etc.

Thoughts?